/*

  Adam Majewski
  adammaj1 aaattt o2 dot pl  // o like oxygen not 0 like zero 
  
  z^6+A*z^2+c
c=(-25165824+7042529*i) * 2^-25
A=(-5162162+25811849*i) * 2^-25
  
coefficients read from input file dumbbell.txt
	degree 6 coefficient = ( 1.000000 +0.000000*i)
	degree 2 coefficient = ( -5162162 +25811849*i) / 2^25
	degree 0 coefficient = ( -25165824 +7042529*i) / 2^25

Input polynomial p(z)=(1+0i)*z^6+(-0.15384441614151000977+0.76925304532051086426i)*z^2+(-0.75+0.20988371968269348145i)

5 critical points found

	cp#0: -0.24073472248875815716,-0.67335945200040758785 . It's critical orbit is escaping

	cp#1: -0.67335945200040758785,0.2407347224887581294 . It's critical orbit is bounded and enters cycle #0 length=18 and it's stability = |multiplier|=0.44474 =attractive
cycle = {
-0.41354178789430684482,0.58233623008786661313 ;
 -0.24139987079110469814,0.22557159004262994362 ; 
 -0.66762351100825734207,0.23359793654192534396 ; 
 -0.62455558023250001831,0.44594269748093573469 ; 
 -0.52191064602206160838,0.55440927484321900209 ;
 -0.2643483421560118285,0.46368951494119226009 ;
 -0.51598018579032589592,0.13520190579783711304 ;
 -0.68005390442212076962,0.39907097482817738276 ;
 -0.61922642315011333647,0.53683595107029358218 ;
 -0.3786598345316821157,0.66121715318625773339 ;
 -0.12392522444160980477,0.056766959109261549976 ;
 -0.74104914546010813847,0.22137970195362727255 ;
 -0.61096648468473280236,0.43419848661563592573 ;
 -0.52000114960119259155,0.5286498139746131919 ;
 -0.3174479972161152741,0.45354543020531506992 ;
 -0.48740107172340202402,0.18783100644450440031 ;
 -0.65233833337812274777,0.3773192327507191024 ;
 -0.59804358278786229342,0.50432516221906276144 ; }

	cp#2: 1.7333369499485122678e-33,0 . It's critical orbit is bounded  and enters cycle #0

	cp#3: 0.67335945200040758785,-0.2407347224887581294 . It's critical orbit is bounded  and enters cycle #0

	cp#4: 0.2407347224887581294,0.67335945200040758785 . It's critical orbit is escaping

  ==============================================
  
  
  Structure of a program or how to analyze the program 
  
  
  ============== Image X ========================
  
  DrawImageOfX -> DrawPointOfX -> ComputeColorOfX 
  
  first 2 functions are identical for every X
  check only last function =  ComputeColorOfX
  which computes color of one pixel !
  
  

   
  ==========================================

  
  ---------------------------------
  indent d.c 
  default is gnu style 
  -------------------



  c console progam 
  
	export  OMP_DISPLAY_ENV="TRUE"	
  	gcc d.c -lm -Wall -march=native -fopenmp
  	time ./a.out > b.txt


  gcc d.c -lm -Wall -march=native -fopenmp


  time ./a.out

  time ./a.out >i.txt
  time ./a.out >e.txt
  
  
  
  
  
  
  convert -limit memory 1000mb -limit disk 1gb dd30010000_20_3_0.90.pgm -resize 2000x2000 10.png

  
  
  
*/

#include <stdio.h>
#include <stdlib.h>		// malloc
#include <string.h>		// strcat
#include <math.h>		// M_PI; needs -lm also
#include <complex.h>
#include <omp.h>		// OpenMP
#include <limits.h>		// Maximum value for an unsigned long long int



// https://sourceforge.net/p/predef/wiki/Standards/

#if defined(__STDC__)
#define PREDEF_STANDARD_C_1989
#if defined(__STDC_VERSION__)
#if (__STDC_VERSION__ >= 199409L)
#define PREDEF_STANDARD_C_1994
#endif
#if (__STDC_VERSION__ >= 199901L)
#define PREDEF_STANDARD_C_1999
#endif
#endif
#endif




/* --------------------------------- global variables and consts ------------------------------------------------------------ */



// virtual 2D array and integer ( screen) coordinate
// Indexes of array starts from 0 not 1 
//unsigned int ix, iy; // var
static unsigned int ixMin = 0;	// Indexes of array starts from 0 not 1
static unsigned int ixMax;	//
static unsigned int iWidth;	// horizontal dimension of array

static unsigned int iyMin = 0;	// Indexes of array starts from 0 not 1
static unsigned int iyMax;	//

static unsigned int iHeight = 10000;	//  
// The size of array has to be a positive constant integer 
static unsigned long long int iSize;	// = iWidth*iHeight; 

// memmory 1D array 
unsigned char *data;
unsigned char *edge;
//unsigned char *edge2;

// unsigned int i; // var = index of 1D array
//static unsigned int iMin = 0; // Indexes of array starts from 0 not 1
static unsigned int iMax;	// = i2Dsize-1  = 
// The size of array has to be a positive constant integer 
// unsigned int i1Dsize ; // = i2Dsize  = (iMax -iMin + 1) =  ;  1D array with the same size as 2D array


static const double ZxMin = -1.3;	//-0.05;
static const double ZxMax = 1.3;	//0.75;
static const double ZyMin = -1.3;	//-0.1;
static const double ZyMax = 1.3;	//0.7;
static double PixelWidth;	// =(ZxMax-ZxMin)/ixMax;
static double PixelHeight;	// =(ZyMax-ZyMin)/iyMax;
static double ratio;


/*
ER = pow(10,ERe);
   AR = pow(10,-ARe);
 */
int ARe ;			// increase ARe until black ( unknown) points disapear 
int ERe ;
double ER;
double ER2;			//= 1e60;
double AR; // bigger values do not works
double AR2;



int IterMax = 100000;


/*
 p(z)=(1+0i)*z^6+(-0.15384441614151000977+0.76925304532051086426i)*z^2+(-0.75+0.20988371968269348145i)
   z^6+A*z^2+c
c=(-25165824+7042529*i) * 2^-25
A=(-5162162+25811849*i) * 2^-25
*/  
complex double A = -0.15384441614151000977+0.76925304532051086426*I; 
complex double c = -0.75+0.20988371968269348145*I;
complex double z18 = -0.24139987079110469814+0.22557159004262994362 *I;


/* colors = shades of gray from 0 to 255 

 unsigned char colorArray[2][2]={{255,231},    {123,99}};
 color = 245;  exterior 
*/
unsigned char iColorOfExterior = 245;
unsigned char iColorOfInterior = 183;
// unsigned char iColorOfInterior2 = 183;
unsigned char iColorOfBoundary = 0;
unsigned char iColorOfUnknown = 5;

// pixel counters
unsigned long long int uUnknown = 0;
unsigned long long int uInterior = 0;
unsigned long long int uExterior = 0;




/* ------------------------------------------ functions -------------------------------------------------------------*/





//------------------complex numbers -----------------------------------------------------





// from screen to world coordinate ; linear mapping
// uses global cons
double
GiveZx (int ix)
{
  return (ZxMin + ix * PixelWidth);
}

// uses globaal cons
double
GiveZy (int iy)
{
  return (ZyMax - iy * PixelHeight);
}				// reverse y axis


complex double
GiveZ (int ix, int iy)
{
  double Zx = GiveZx (ix);
  double Zy = GiveZy (iy);

  return Zx + Zy * I;




}



double cabs2(complex double z){

	return creal(z)*creal(z)+cimag(z)*cimag(z);


}



int IsEscaping(complex double z){

	if (cabs2 (z) > ER2) return 1;
	return 0;
}


int IsAttracting(complex double z){

	if (cabs2 (z - z18) < AR2) return 1;
	return 0;
}













// ****************** DYNAMICS = trap tests ( target sets) ****************************


/* -----------  array functions = drawing -------------- */

/* gives position of 2D point (ix,iy) in 1D array  ; uses also global variable iWidth */
unsigned int
Give_i (unsigned int ix, unsigned int iy)
{
  return ix + iy * iWidth;
}



// f(z)=1+z−3z2−3.75z3+1.5z4+2.25z5
unsigned char
ComputeColor_Fatou (complex double z, int IterMax)
{



	complex double z2;
	complex double z6;
	


  int i;			// number of iteration
  for (i = 0; i < IterMax; ++i)
    {


	z2 = z*z;
	z6 = z2*z2*z2;

      	z =  z6+A*z2+c; // complex iteration  z^6+A*z^2+c
	
	//z = z*z;
      if (IsEscaping(z)) // escaping = exterior
	{
	  uExterior += 1;
	  return iColorOfExterior;
	}			
	
	if ( IsAttracting(z) ) 
	{
		uInterior +=1;
		return iColorOfInterior;
	}
	

    }

  uUnknown += 1;
  return iColorOfUnknown;


}





// plots raster point (ix,iy) 
int
DrawFatouPoint (unsigned char A[], int ix, int iy, int IterMax)
{
  int i;			/* index of 1D array */
  unsigned char iColor = 0;
  complex double z;


  i = Give_i (ix, iy);		/* compute index of 1D array from indices of 2D array */
  z = GiveZ (ix, iy);
  iColor = ComputeColor_Fatou (z, IterMax);
  A[i] = iColor;		// interior

  return 0;
}




// fill array 
// uses global var :  ...
// scanning complex plane 
int
DrawFatouImage (unsigned char A[], int IterMax)
{
  unsigned int ix, iy;		// pixel coordinate 

  printf ("compute Fatou image \n");
  // for all pixels of image 
#pragma omp parallel for schedule(dynamic) private(ix,iy) shared(A, ixMax , iyMax, uUnknown, uInterior, uExterior)
  for (iy = iyMin; iy <= iyMax; ++iy)
    {
      fprintf (stderr, " %d from %d \r", iy, iyMax);	//info 
      for (ix = ixMin; ix <= ixMax; ++ix)
	DrawFatouPoint (A, ix, iy, IterMax);	//  
    }

  return 0;
}


//=========








// ***********************************************************************************************
// ********************** edge detection usung Sobel filter ***************************************
// ***************************************************************************************************

// from Source to Destination
int ComputeBoundaries(unsigned char S[], unsigned char D[])
{
 
  unsigned int iX,iY; /* indices of 2D virtual array (image) = integer coordinate */
  unsigned int i; /* index of 1D array  */
  /* sobel filter */
  unsigned char G, Gh, Gv; 
  // boundaries are in D  array ( global var )
 
  // clear D array
  memset(D, iColorOfExterior, iSize*sizeof(*D)); // for heap-allocated arrays, where N is the number of elements = FillArrayWithColor(D , iColorOfExterior);
 
  // printf(" find boundaries in S array using  Sobel filter\n");   
#pragma omp parallel for schedule(dynamic) private(i,iY,iX,Gv,Gh,G) shared(iyMax,ixMax)
  for(iY=1;iY<iyMax-1;++iY){ 
    for(iX=1;iX<ixMax-1;++iX){ 
      Gv= S[Give_i(iX-1,iY+1)] + 2*S[Give_i(iX,iY+1)] + S[Give_i(iX-1,iY+1)] - S[Give_i(iX-1,iY-1)] - 2*S[Give_i(iX-1,iY)] - S[Give_i(iX+1,iY-1)];
      Gh= S[Give_i(iX+1,iY+1)] + 2*S[Give_i(iX+1,iY)] + S[Give_i(iX-1,iY-1)] - S[Give_i(iX+1,iY-1)] - 2*S[Give_i(iX-1,iY)] - S[Give_i(iX-1,iY-1)];
      G = sqrt(Gh*Gh + Gv*Gv);
      i= Give_i(iX,iY); /* compute index of 1D array from indices of 2D array */
      if (G==0) {D[i]=255;} /* background */
      else {D[i]=0;}  /* boundary */
    }
  }
 
   
 
  return 0;
}



// copy from Source to Destination
int CopyBoundaries(unsigned char S[],  unsigned char D[])
{
 
  unsigned int iX,iY; /* indices of 2D virtual array (image) = integer coordinate */
  unsigned int i; /* index of 1D array  */
 
 
  //printf("copy boundaries from S array to D array \n");
  for(iY=1;iY<iyMax-1;++iY)
    for(iX=1;iX<ixMax-1;++iX)
      {i= Give_i(iX,iY); if (S[i]==0) D[i]=0;}
 
 
 
  return 0;
}
















// *******************************************************************************************
// ********************************** save A array to pgm file ****************************
// *********************************************************************************************

int
SaveArray2PGMFile (unsigned char A[], int a, int b,  int c, char *comment)
{

  FILE *fp;
  const unsigned int MaxColorComponentValue = 255;	/* color component is coded from 0 to 255 ;  it is 8 bit color file */
  char name[100];		/* name of file */
  snprintf (name, sizeof name, "%d_%d_%d", a, b, c );	/*  */
  char *filename = strcat (name, ".pgm");
  char long_comment[200];
  sprintf (long_comment, "%s\tJulia set for p(z)=z^6+A*z^2+c ", comment);





  // save image array to the pgm file 
  fp = fopen (filename, "wb");	// create new file,give it a name and open it in binary mode 
  fprintf (fp, "P5\n # %s\n %u %u\n %u\n", long_comment, iWidth, iHeight, MaxColorComponentValue);	// write header to the file
  fwrite (A, iSize, 1, fp);	// write array with image data bytes to the file in one step 
  fclose (fp);

  // info 
  printf ("File %s saved ", filename);
  if (long_comment == NULL || strlen (long_comment) == 0)
    printf ("\n");
  else
    printf (". Comment = %s \n", long_comment);

  return 0;
}




int
PrintCInfo ()
{

  printf ("gcc version: %d.%d.%d\n", __GNUC__, __GNUC_MINOR__, __GNUC_PATCHLEVEL__);	// https://stackoverflow.com/questions/20389193/how-do-i-check-my-gcc-c-compiler-version-for-my-eclipse
  // OpenMP version is displayed in the console : export  OMP_DISPLAY_ENV="TRUE"

  printf ("__STDC__ = %d\n", __STDC__);
  printf ("__STDC_VERSION__ = %ld\n", __STDC_VERSION__);
  printf ("c dialect = ");
  switch (__STDC_VERSION__)
    {				// the format YYYYMM 
    case 199409L:
      printf ("C94\n");
      break;
    case 199901L:
      printf ("C99\n");
      break;
    case 201112L:
      printf ("C11\n");
      break;
    case 201710L:
      printf ("C18\n");
      break;
      //default : /* Optional */

    }

  return 0;
}


int
PrintProgramInfo ()
{


  // display info messages
  printf ("Numerical approximation of Julia set for p(z)=z^6+A*z^2+c = z^6+(-0.15384441614151000977+0.76925304532051086426i)*z^2+(-0.75+0.20988371968269348145i) \n");
  //printf ("iPeriodParent = %d \n", iPeriodParent);
  //printf ("iPeriodOfChild  = %d \n", iPeriodChild);
  //printf ("parameter c = ( %.16f ; %.16f ) \n", creal (c), cimag (c));

  printf ("Image Width = %f in world coordinate\n", ZxMax - ZxMin);
  printf ("PixelWidth = %.16f \n", PixelWidth);
  printf ("AR = %.16f = %f *PixelWidth\n", AR, AR / PixelWidth);


  printf("pixel counters\n");
  printf ("uUnknown = %llu\n", uUnknown);
  printf ("uExterior = %llu\n", uExterior);
  printf ("uInterior = %llu\n", uInterior);
  printf ("Sum of pixels  = %llu\n", uInterior+uExterior + uUnknown);
  printf ("all pixels of the array = iSize = %llu\n", iSize);


  // image corners in world coordinate
  // center and radius
  // center and zoom
  // GradientRepetition
  printf ("Maximal number of iterations = iterMax = %d \n", IterMax);
  printf ("ratio of image  = %f ; it should be 1.000 ...\n", ratio);
  //




  return 0;
}






// *****************************************************************************
//;;;;;;;;;;;;;;;;;;;;;;  setup ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
// **************************************************************************************

int
setup ()
{

  printf ("setup start\n");






  /* 2D array ranges */

  iWidth = iHeight;
  iSize = iWidth * iHeight;	// size = number of points in array 
  // iy
  iyMax = iHeight - 1;		// Indexes of array starts from 0 not 1 so the highest elements of an array is = array_name[size-1].
  //ix

  ixMax = iWidth - 1;

  /* 1D array ranges */
  // i1Dsize = i2Dsize; // 1D array with the same size as 2D array
  iMax = iSize - 1;		// Indexes of array starts from 0 not 1 so the highest elements of an array is = array_name[size-1].

  /* Pixel sizes */
  PixelWidth = (ZxMax - ZxMin) / ixMax;	//  ixMax = (iWidth-1)  step between pixels in world coordinate 
  PixelHeight = (ZyMax - ZyMin) / iyMax;
  ratio = ((ZxMax - ZxMin) / (ZyMax - ZyMin)) / ((double) iWidth / (double) iHeight);	// it should be 1.000 ...

  ER = 2.0; //pow (10, ERe);
  ER2 = ER*ER;
  AR = PixelWidth/10.0;
  AR2 = AR * AR;



  	/* create dynamic 1D arrays for colors ( shades of gray ) */
  	data = malloc (iSize * sizeof (unsigned char));

	edge = malloc (iSize * sizeof (unsigned char));
  	if (data == NULL || edge == NULL)
    		{
      			fprintf (stderr, " Could not allocate memory");
      			return 1;
    		}





 


  fprintf (stderr," end of setup \n");

  return 0;

}				// ;;;;;;;;;;;;;;;;;;;;;;;;; end of the setup ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;




int
end ()
{


  fprintf (stderr, " allways free memory (deallocate )  to avoid memory leaks \n");	// https://en.wikipedia.org/wiki/C_dynamic_memory_allocation
  free (data);
  free(edge);


  PrintProgramInfo ();
  PrintCInfo ();
  return 0;

}

// ********************************************************************************************************************
/* -----------------------------------------  main   -------------------------------------------------------------*/
// ********************************************************************************************************************

int
main ()
{
  	setup ();


  	DrawFatouImage (data, IterMax);	// first find Fatou
  	SaveArray2PGMFile (data, iWidth, IterMax, 0, "Fatou, name = iWidth_IterMax_n");
  
  	ComputeBoundaries(data,edge);
  	SaveArray2PGMFile (edge, iWidth, IterMax, 1, "Boundaries of Fatou; name = iWidth_IterMax_n"); 
  
  	CopyBoundaries(edge,data);
  	SaveArray2PGMFile (data, iWidth, IterMax, 2, "Fatou with voundaries; name = iWidth_IterMax_n"); 
  
  

  end ();

  return 0;
}